82 



MEMOIRS NATIONAL ACADEMY OF SCIENCES. 



[Vol. XIV. 



Table 1 (c). 



The analysis by the method of sequences of the 80 noncongruent systems derived by Mr. 

 Cole in Part 4, shows that 77 of these systems are congruent either to systems derived in Part 1 

 by means of operators of their groups; or to systems derived from the former, in Part 3, by 

 means of quadi-angular or hexagonal transformations. 



The names or numbers of these 77 pairs of equivalent systems and the substitution wliich 

 transforms each of Mr. Cole's systems into its equivalent system are given below. 



I, l=IIIAby si 



I, 2=IIIBby s; 



I, 3=IIICby s; 



I, 4=IIEby s\ 



I, 5=IVAby s: 



I, 6=IIAby S-: 



I, 7=VAby s; 



I, 8=IVBby s; 



I, 9=IICby s] 



I, 10=1 ID by s; 



I, ll=VIBby s; 



I, 12=VID by si 



I, 13=VC by s; 

 I, 14=VD by 



-0 



1 



a 



1 2 

 6 a 



1 2 



6 

 9 

 6 

 / 

 6 



2 

 6 



2 

 b 



1 2 



d / 



2 



d 



3 4 



6 d 



3 4 



e d 



3 4 



c d 



3 4 



6 c 



9 / 



5 6 



1 4 



5 6 



? « 



5 6 



/ « 



5 6 



e / 



5 6 



e a 



5 

 c 



a f 



3 4 



rf / 



3 4 



c 6 



3 4 



c a 



8 9 



1 2 



8 9 



1 2 



8 9 



1 2 



8 9 



9 

 3 



8 9 

 4 5 



10 11 

 3 4 



10 11 

 3 4 



10 11 

 3 4 



10 11 



9 f 



10 11 



3 4 



10 11 



7 8 



10 11 



5 8 



10 11 



3 7 



10 11 



8 7 



10 11 

 3 6 



10 11 



5 6 



10 11 

 3 8 



10 11 



6 5 



10 11 



5 7 



14 15 



14 15 



14 15 

 8 7 



14 15 



14 15 



12 13 



4 8 



12 13 



5 6 



12 13 



1 7 



12 13 



2 3 



12 13 



7 5 



12 13 



4 8 



12 13 



8 3 



5) 



?) 



) 



) 



5) 



14 15 \ 

 4 3/ 



14 15 \ 

 6 7/ 



14 15 \ 

 & 2 ) 



14 15 \ 

 2 1 ) 



14 15 "S 

 2 8/ 



14 15 \ 

 4 i ) 



14 15 \ 

 1 6 ) 



14 15 ^ 

 1 3 



14 15 

 6 2 



I) 



